The ROM files go into /system. Your apps go into /data. They are totally separate.
However, there is most definitely a space issue. If you have lots of apps, your dalvik cache is going to fill up internal storage. alpha7 will automagically use your sd-ext partition for the dalvik cache if it exists. It's highly recommended to have an sd-ext partition for this reason alone. Additionally, in the next update, I'm going to do the same for apps. So if you have a decent size sd-ext (say, 1gb or more) you'll have more space for apps than a sane person will ever use.
I don't have links handy so I'll let others point out the best sd-ext resources and tutorials.